Outlier-robust spectral estimation for spatial lattice processes

The presence of outliers in spatial data can seriously affect estimates of second-order properties such as auto-covariance functions (ACF's) and spectra. This paper concerns spatial data in the form of continuous measurements on a rectangular grid. We introduce the spatial additive outlier model, which incorporates flexibility to produce both 'isolated' and 'patchy' spatial distributions of outliers. The bias in the ACF and spectrum caused by contamination is analysed, and a non-model-based data-cleaner is proposed. The cleaned data may be used as input to standard routines yielding bias-robust estimates of the required functions. The method compares favourably with other procedures in the absence of contamination and in the presence of isolated outliers. It has an added advantage of being robust to patchy distributions of outliers. Illustrative examples of the application of the method are presented using simulated data and data on the concentration of copper in the soil in UK grid squares.